Question: Subtract the following rational expressions. $\dfrac{6z+5}{13z^2+2z}-\dfrac{7z-2}{13z^2+2z}=$
Answer: We want to subtract two rational expressions whose denominators are equal. We can do this by subtracting the numerators and keeping the denominator the same. [Does this fit with how we subtract rational numbers?] $\begin{aligned} &\phantom{=}\dfrac{6z+5}{13z^2+2z}-\dfrac{7z-2}{13z^2+2z} \\\\ &=\dfrac{(6z+5)-(7z-2)}{13z^2+2z} \\\\ &=\dfrac{6z+5-7z+2}{13z^2+2z} \\\\ &=\dfrac{-z+7}{13z^2+2z} \end{aligned}$ In conclusion, $\dfrac{6z+5}{13z^2+2z}-\dfrac{7z-2}{13z^2+2z}=\dfrac{-z+7}{13z^2+2z}$